Question

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\overrightarrow{E}=E_0\hat{j}$ and $\overrightarrow{B}=B_0\hat{j}$. At time t = 0, this charge has velocity $\overrightarrow{v}$ in the x-y plane, making an angle $\theta$ with the x axis.
Which of the following option(s) is(are) correct for time t > 0 ?

• A. If $\theta =0^{\circ }$, the charge moves in a circular path in the x-z plane.
• B. If $\theta =0^{\circ }$ , the charge undergoes helical motion with constant pitch along the y-axis.
• C. If $\theta ={10}^{\circ }$, the charge undergoes helical motion with its pitch increasing with time, along the y-axis
• D. If $\theta ={90}^{\circ }$, the charge undergoes linear but accelerated motion along the y-axis.

Answer 1

Answer: (C), (D)

The correct options are
C If $\theta ={10}^{\circ }$, the charge undergoes helical motion with its pitch increasing with time, along the y-axis
D If $\theta ={90}^{\circ }$, the charge undergoes linear but accelerated motion along the y-axis.

If $\theta ={90}^0$ $B$ exerts no force on $q$ as $sin90=0$

If $\theta ={10}^0$ the charge particle move in helix due to the electric force along Y-axis.